Abstract

A geometric approach to investigation of quantum entanglement is advocated. Analyzing the space of pure states of a bipartite system we show how an entanglement measure of a gives state can be related to its distance to the closest separable state. We study geometry of the (N² - 1)-dimensional convex body of mixed quantum states acting on an N-dimensional Hilbert space and demonstrate that it belongs to the class of sets of a constant height. The same property characterizes the set of all separable states of a two-qubit system. These results contribute to our understanding of quantum entanglement and its dynamics.

© 2008 Optical Society of America